Vangipuram Lakshmikantham

This chapter introduces the theory of lower and upper solutions coupled with the monotone iterative technique and the method of generalized quasilinearization for elliptic boundary value problems (BVPs), and therefore forms the basis for the rest of the book, where the essential ideas are extended to parabolic and hyperbolic initial boundary value problems (IBVPs), by classical as well as variational approaches.

— from MONOTONE FLOWS AND RAPID CONVERGENCE FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS